When coherent electromagnetic waves with wavelength $=120$m$=120$m are incident on a single slit of width aa$,$ the width of the central maximum on a tall screen $1\mathrm{.}50$ mm from the slit is $90\mathrm{.}0$ cm$.$For the same slit and screen, for what wavelength of the incident waves is the width of the central maximum $180\mathrm{.}0$ cmcm$,$ double the value when $=120$m$=120$m$?$